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Abstract Local adaptation can lead to elevated genetic differentiation at the targeted genetic variant and nearby sites. Selective sweeps come in different forms, and depending on the initial and final frequencies of a favored variant, very different patterns of genetic variation may be produced. If local selection favors an existing variant that had already recombined onto multiple genetic backgrounds, then the width of elevated genetic differentiation (high FST) may be too narrow to detect using a typical windowed genome scan, even if the targeted variant becomes highly differentiated. We, therefore, used a simulation approach to investigate the power of SNP-level FST (specifically, the maximum SNP FST value within a window, or FST_MaxSNP) to detect diverse scenarios of local adaptation, and compared it against whole-window FST and the Comparative Haplotype Identity statistic. We found that FST_MaxSNP had superior power to detect complete or mostly complete soft sweeps, but lesser power than full-window statistics to detect partial hard sweeps. Nonetheless, the power of FST_MaxSNP depended highly on sample size, and confident outliers depend on robust precautions and quality control. To investigate the relative enrichment of FST_MaxSNP outliers from real data, we applied the two FST statistics to a panel of Drosophila melanogaster populations. We found that FST_MaxSNP had a genome-wide enrichment of outliers compared with demographic expectations, and though it yielded a lesser enrichment than window FST, it detected mostly unique outlier genes and functional categories. Our results suggest that FST_MaxSNP is highly complementary to typical window-based approaches for detecting local adaptation, and merits inclusion in future genome scans and methodologies.